The most efficient way to constrain the photon mass (mph) is related to observations of large‐scale magnetic fields in space physics and astrophysics. This approach is based on the change in the Ampere law caused by the finite mph. In 1990s, a consistent set of MHD equations allowing for the finite mph has been written and later used to analyze the solar wind data from the Voyager 1 and 2 missions. This lead to an estimate mph<1.5×10−51g, the value currently recommended by the bi‐annual compendium of the Particle Data Group. The further progress in constraining the photon mass may come from considering the dynamics of large‐scale magnetic fields in astrophysics, in particular, the magnetic field of galaxies. The paper is concerned with related opportunities and challenges, including the problem posed by the simultaneous presence of large‐scale and much stronger small‐scale magnetic fields. Effects of recycling of the interstellar plasma involving dense molecular clouds, protostars and supernovae explosions are discussed. Possible approaches to pushing the upper bound to a limit well below 10−51g are discussed.

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